On signed p-Kostka numbers and the indecomposable signed Young\n permutation modules

2015/05/05 by Eugenio Giannelli, Kay Jin Lim, Giannelli, Eugenio +5
Mathematics · #20C30 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1505.01073

openalex publication_date 2015/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence and main properties of signed Young modules for the\nsymmetric group, using only basic facts about symmetric group representations\nand the Brou 'e correspondence. We then prove new reduction theorems for the\nsigned p-Kostka numbers, defined to be the multiplicities of signed Young\nmodules as direct summands of signed Young permutation modules. We end by\nclassifying the indecomposable signed Young permutation modules and determining\ntheir endomorphism algebras.\n

Related

• On signed p-Kostka matrices
• Young module multiplicities and classifying the indecomposable Young\n permutation modules
• Signed Young Modules and Simple Specht Modules
• Irreducible Specht modules are signed Young modules
• A new approach to the representation theory of the symmetric groups, III: Induced representations and the Frobenius--Young correspondence